Combine sliced celery, carrots, potatoes, salt, and water to cover in a skillet or pot. Cover and bring to a boil. When boiling, uncover and reduce to medium-low and cook until most of the liquid is evaporated.
Meanwhile, prepare the fish. In shallow dish or pie pan, combine panko, lime zest, parmesan, parsley, salt, and pepper; mix well. In another shallow dish, combine egg and lemon juice; beat well. First, add the fish fillet to the egg mixture. Make sure the fish is well coated. Then bread 2 sides of the fish with the panko mix. Set aside.
When the veggies are soft, transfer to a bowl and keep the cooking water for the sauce.
In the same skillet or pot melt butter. Then stir in flour; cook, stirring, for 1 minute.
Gently add milk and cooking water; cook, stirring all of the ingredients together, until creamy. Add grated cheese and stir until melted. Season with salt, nutmeg, and pepper to taste. Transfer to an oven-safe dish.
Mix panko, spring onions, and parsley; sprinkle over the celery mixture and broil in the oven until golden.
Meanwhile, heat cooking oil over medium heat and cook breaded fish on both sides until golden.
Serve with celery-carrot gratin.